Preheat oven to 375 degrees. Butter an 8-inch square (2-quart) baking dish; set aside. In a large saucepan, combine cream, goat cheese, and garlic; season with salt and pepper.

Peel potatoes and slice crosswise 1/8 inch thick; add to cream mixture as you work. Bring to a boil. Reduce to a simmer; cook until potatoes are crisp-tender, 12 to 15 minutes.

Transfer mixture to prepared baking dish; using a spatula, press potatoes into cream to cover. Place dish on a rimmed baking sheet; bake until golden and potatoes are tender, 20 to 25 minutes.

Fifteen minutes before potatoes are finished baking, heat a large skillet over medium-high. Season steaks on both sides with salt and pepper; cook, 6 to 7 minutes per side for medium-rare (if browning too quickly, reduce heat when cooking second side). Transfer to a plate, cover loosely with aluminum foil, and set aside. Keep skillet with any browned bits for wine sauce.

Make wine sauce: Add wine to skillet; boil over medium-high heat until syrupy, 3 to 4 minutes. Whisk in mustard. (For a smoother sauce, pour mixture through a fine-mesh sieve, discard any browned bits, and return liquid to skillet.) Stir in capers and any juices from resting steaks; season with salt and pepper. Serve steaks with wine sauce and potato gratin.

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